The present invention relates to a linear accelerator for accelerating charged particles, and more particularly to a wake field accelerator which is a high gradient linear accelerator well suited to the miniaturization of the whole accelerator.
The basic idea of a wake field accelerator, which is in the limelight as a high gradient linear accelerator of the next generation, is traced back to an automatic accelerator by M. Friedman (Naval Research Laboratory in U.S., 1973). A "wake field" is a transient electromagnetic field which is established by the electromagnetic interaction between a bunch of charged particles and a conductor wall surrounding them and which remains behind the bunch of charged particles. In the present invention, a voltage generated in the wake field shall be called a "wake field voltage". The "wake field accelerator" is an apparatus in which a bunch of charged particles in a small number (hereinbelow, termed "charged particle bunch to-be-accelerated)" that succeed a bunch of charged particles having excited the wake field (hereinbelow, termed "driving charged particle bunch)" are accelerated by a high electric field owned by the wake field. Important factors which govern the performance of the wake field are a transformer ratio R and an energy extraction efficiency .eta..
The "transformer ratio" is the ratio of the maximum acceleration voltage which the charged particle bunch to-be-accelerated undergoes, to the maximum deceleration voltage which the driving charged particle bunch undergoes at the wake field voltage. As the transformer ratio R is higher, the relative ability of the high field acceleration rises more.
On the other hand, the "energy extraction efficiency" indicates the proportion of energy by which the driving charged particle bunch has actually excited the wake field, to the maximum excitation energy which can be stored in the wake field. The energy by which the driving charged particle bunch excites the wake field, is equal to the sum of energies which individual driving charged particles lose due to deceleration voltages V.sub.m (t) induced in the wake field by the driving charged particle.
The, maximum excitation energy is energy which is stored in the wake field when the individual charged particles are decelerated by the maximum deceleration voltage V.sub.m.sup.- realizable in the wake field. Accordingly, the energy extraction efficiency .eta. is evaluated by the following equation: ##EQU1##
Here, I(t): current formed by the driving charged particle bunch at a time t,
V.sub.m (t): deceleration voltage in the wake field at the time t, PA0 V.sub.m.sup.- : maximum deceleration voltage which the driving charged particle bunch undergoes. PA0 I.sub.o : constant, PA0 .omega.: resonant angular frequency of the fundamental mode of the cavity.
Accordingly, wake field accelerator of favorable energy extraction efficiency is an accelerator which can form the maximum deceleration voltage quickly and which can thereafter maintain it so as to decelerate the driving charged particles.
An example of a wake field accelerator of high transformer ratio and high energy extraction efficiency is a wake field accelerator by K. L. F. Base et al., which descended from the autoaccelerator by M. Friedman. It is detailed in "SLAC-PUB 3662 (Apr. 1985)" which is the research report of Stanford Linear Accelerator Center in the U.S. Here, Base's wake field accelerator will be briefly explained.
A bunch of electrons are processed so as to excite a wake field and a bunch of electrons to be accelerated are caused to travel along the center axis of an axially-symmetric cavity. On this occasion, current I(t) formed by the driving electron bunch which is caused to flow for a time interval T is changed as indicated by the following equation: ##EQU2##
Here,
The situation of the time-variation of a wake field voltage V(t) on the center axis of the cavity as based on the wake field excited on this occasion, is illustrated in FIG. 2(1) or FIG. 2(2). A broken line in the figure denotes the current I(t). As illustrated in FIG. 2(1) or FIG. 2(2), the wake field voltage V(t) takes minus values and acts as a deceleration voltage for 0.ltoreq.t.ltoreq.T. That is, the electron bunch exciting the wake field or the driving electron bunch is decelerated at all times. In consequence, the electron bunch always continues to supply energy to the wake field, and the wake field continues to grow every moment.
In the prior art, the Joule heat loss of an electromagnetic field on the conductor wall surface of the cavity is not taken into account. With the prior art, it is asserted that the transformer ratio R becomes: ##EQU3## thereby increasing without limitation in proportion to the time interval T. Due to the Joule heat loss of the electromagnetic field on the conductor wall surface of the cavity, however, energy is lost, and the energy imparted by the driving electron bunch is not entirely stored in the wake field. Accordingly, letting n=.gamma.T (where .gamma. denotes an attenuation factor which is based on the finite conductivity of the cavity, and which becomes ##EQU4## in terms of the Q-value of the cavity), the actual transformer ratio R is approximately given by: ##EQU5## and it becomes saturated to R=2 Q for n.fwdarw..infin.. The n-dependency of the transformer ratio R is illustrated in FIG. 3(1). In addition, n can be expressed an n= ##EQU6## in terms of the velocity of light c and a wavelength .lambda. because .omega.=2.pi.c/.lambda. holds. Here, c.multidot.T corresponds to the beam length of the driving electron bunch. Therefore, a small value of the quantity n signifies that the required beam length of the driving electron bunch is short.
On the other hand, the energy extraction efficiency .eta. is higher at I(t)=I.sub.2 (t) than at I(t)=I.sub.1 (t) and is approximately given by: ##EQU7## With the prior art, it is asserted that, for ##EQU8## (that is, ##EQU9## where a wavy line signifies "nearly equal)", the energy extraction efficiency .eta. is substantially 100% irrespective of n. Also here, however, the deceleration voltage V.sub.m (t) in FIG. 2(2) does not behave as indicated by a solid line, but rather as indicated by a broken line, on account of the Joule heat loss on the wall surface of the cavity. Accordingly, the energy extraction efficiency .eta. defined by Eq. (1) is expressed by Eq. (6), and it gradually lowers down to a value of 66.7% for n&gt;1. The n-dependency of the energy extraction efficiency .eta. is illustrated in FIG. 3(2).
As stated above, the prior art has the problem that, since the Joule heat loss on the wall surface of the cavity is not considered, actually the transformer ratio R and the energy extraction efficiency .eta. decrease. The second problem ascribable to the Joule heat loss on the wall surface of the cavity is that, when the time interval T for which the current is caused to flow is lengthened, the energy extraction efficiency .eta. lowers cover though the transformer ratio R increases.